There is more information in the Grand Alliance books on each mini faction. Not a huge amount, but they do put the faction into a place in the world.
However, it is the kind've fluff that should be on each sub-factions landing page for each sub-faction on the website. The problem is, the current website is really just a webstore and everything is just filters on what products the user should see. So while you can select Order Serpentis on the store, you could also click Order Draconis as well and then what info should it be showing.
Personally I think GW should invest in an actual 'Age of Sigmar' website in a similar fashion to what they're doing with some of their boxed games. This website can give a brief history up until now, details on the goals and agendas of ALL of factions in the game, and of course, links to where to buy the models from the online store.